A Price Theory of Multi-Sided Platforms

Transcription

1 A Price Theory of E. Glen Weyl Harvard Society of Fellows and Toulouse School of Economics Academic Slides January 2011

2 AmEx and the Times Introduction Framework Solving the model American Express and New York Times Both two-sided markets but... AmEx Times Loyalists value acceptance more than marginals Imperfect internalization because no discrimination Higher card-holder price = more cross-subsidies Classic 2sms logic (Rochet and Tirole 2003) Loyalists hate advertising more Ad prices too low? Higher subscription price = less ads, higher prices Ignored or assumed away by current analysis Today: full Rochet and Tirole (2006) accommodates both Crucial difference is source of user heterogeneity

3 Outline Basic Argument Introduction Framework Solving the model 1 Basic argument Two-sided markets Framework Solution approach 2 Applications Pricing Comparative statics Scale-Income model 3 Policy Generalization Conclusion

4 What is a two-sided market? Introduction Framework Solving the model Definition of 2sms controversial For me: modeling approach (not market-type), useful when 1 Two distinct, discriminable groups 2 Cross-network effects; both participations matter for both Components patented = cell phone=vertical monopoly 3 Bilateral market power No monopsony = supermarket=distributor Otherwise much easier approaches Examples: payments, advertising platforms and... 1 Software platforms (operating systems, video games, etc.) 2 Internet service provision 3 Commercial intermediation (EBay, stock markets) 4 Advertising providers (Google, Yahoo!, etc.) 5 Rating agencies (credit, user information, etc.)

5 Assumptions Basic Argument Introduction Framework Solving the model Today I will maintain three prominent assumptions: 1 Monopoly: but most markets are oligopoly 2 Homogeneous externalities But rich readers are worth more to advertisers 3 Valuations exogenous, no direct interactions But application developers value determined by price My next to presentations will be about relaxing these Today: RT2006 model has additional assumptions: 1 Network effects across not within, only two sides = No externality heterogeneity by side differentiation 2 Affine values and random sample I ll drop these in the generalization at end of talk

6 Model primitives Basic Argument Introduction Framework Solving the model 1 Demand 2 Supply Two groups of users A and B, each unit mass Users heterogeneous in two values Fixed membership benefit/cost B I i (Armstrong) Interaction benefit/cost b I i per partner (RT2003) U I i = B I i + b I i NJ P I ( N J) Arbitrary correlations allowed (only smoothness) Membership costs C I and interaction cost c Only uniform pricing (no discrimination) 3 Equilibrium 1 Platform chooses tariff anticipating... 2 Induced equilibrium determines participation/demand

7 Preferences Basic Argument Introduction Framework Solving the model ( Figure : U ) i A N B for various RT2003 (left) and Armstrong (right) preferences. This illustrates the two dimensions of heterogeneity: interaction and membership values, respectively.

8 Introduction Framework Solving the model Coordination and the insulating tariff Potential multiplicity (for some tariffs) But unique equilibrium prices P I ( N I, N J) So multiplicity inessential Only possible failure to implement desired allocation Evans and Schmalensee (2009) s failure to launch Smart platform always achieves desired allocation uniquely Set insulating tariff P I ( N J) P I (ÑI, N J ) For Armstrong, full insurance (Dybvig and Spatt 1983) For RT2003, strategic insulation (interaction fee) Possible dynamic implementation Thus we can ignore coordination problem Sometimes firms refrain; why? Platform chooses allocation, tariff details irrelevant No more fixed point: optimization simplifies analysis

9 Visualizing demand Introduction Framework Solving the model B A ba 5 Figure : The set of users participating on side A when half of users participate on side B and P A = 5 and 6 respectively

10 Pigouvian pricing Pricing Comparative statics An Example: the Scale-Income model Social value from platform V A ( N A, N B) + V B ( N B, N A) C A N A C B N B cn A N B P I = } C I + {{ cn J } b } J {{ N J } private cost external benefit b I average interaction benefit of participating users Standard Pigou Special cases 1 Armstrong: c 0, b I i b I P I = C I b J N J 2 RT2003: C I, B I i 0 All interaction so b I = p I + s I V I p A + p B c = s A = s B N J

11 Profit-maximizing pricing Pricing Comparative statics An Example: the Scale-Income model Equate marginal revenues and costs P I µ I }{{} classical marginal revenue + bj N J }{{} cross-marginal revenue = C I + cn J }{{} marginal cost µ I classic market power b I average interaction benefit of marginal users Two distortions from inability to price discriminate 1 Classical market power upwards 2 Spence distortion: internalize wrong quality preference Then you were a tourist... More important in 2sms May go in either direction (credit cards v. newspapers) Driven by source of user heterogeneity Armstrong P I = C I b J N J + µ I : no Spence Or RT2003 p A + p B c = m A = m B : Spence upward

12 Ramsey-Oum-Tretheway pricing Pricing Comparative statics An Example: the Scale-Income model Optimum may require subsidies If these infeasible, Ramsey pricing is second best Ramsey pricing+externalities=oum and Tretheway (1988) λ = ) P I = C I + cn J (λ b J + [1 λ]b J N J + λµ I ( ) K + b A +b B c N A N B ) N A µ A +N B µ B + (b A +b B b A b B N A N B

13 Pricing Comparative statics An Example: the Scale-Income model Second-order properties and conditions Conditions necessary, but insufficient Need some second-order/concavity condition Propose first for RT2006 model ρ I is pass-through rate holding fixed N J χ is cross-partial (substitutes v. complements) Two-sided contraction µ A µ B > ρ A ρ B χ 2 ( N A, N B) N A N B Necessary & sufficient for first-order solution ( C A, C B) Armstrong χ = b A + b B c so µ A µ B N A N B > ρ A ρ B ( b A + b B) 2 RT2003 χ = m A = m B so 1 > ρ A ρ B

14 Complements v. substitutes Pricing Comparative statics An Example: the Scale-Income model Most basic comparative static: seesaw principle RT2006 seem to think it is general Not clear what it means more broadly: what prices? Equivalent to substitution of participation rates in RT2003 Natural way to generalize...but not true generally Some definitions 1 α 2 β µ b µ B ( ba + b B c) N A N B π marginal interaction surplus ratio interaction heterogeneity ratio Decompose µ I = µ Ĩ b + µĩ B and aggregate µ = NA µ A + N B µ B Substitutes if µ B 0 or β > α If µ b > 0, complements if α > β, independent if α = β Change in cross-subsidy versus scaling Again source of heterogeneity, link to normative properties RT2003 = substitutes, Armstrong = complements

15 Welfare effects Basic Argument Pricing Comparative statics An Example: the Scale-Income model For me: 2sms = externalities in absence of transfers But other say holding fixed price indirect network effects But what price? Model says only P I ( N J ) matters With insulating, never externalities in this sense Perhaps more sensible: does I want C J to rise or fall? Sign is same as b I b I + ρ I χ Direct and indirect Ambiguous effect of source of heterogeneity Crucial: infra-marginal v. marginal But pass-through related to this as V = ρµd (other talk) For example: RT2003 sign determined by ρ I Third derivative of log-demand important Even possible that C I good for I Again, when infra-marginal dominates marginal (by a lot)

16 Unidimensional models Pricing Comparative statics An Example: the Scale-Income model Can do any comparative static, but clearly ambiguity Resolved, analysis more concrete through more structure Natural direction: only one dimension of heterogeneity Armstrong and RT2003 examples But Armstrong heterogeneity rarely plausible RT2003 restricts membership costs/benefits implausibly Easily solved: only source of heterogeneity matters Generalized RT2003 model potentially well-suited Analyzed in paper; quite similar to RT2003 But still many markets seem mismatched to these So here: new models, perhaps more realistic First is Hybrid: one side RT2003, one Armstrong May fit some better (advertising, software platforms) But better is one I ll discuss in more detail

17 Scale-Income model Pricing Comparative statics An Example: the Scale-Income model Idea: homogeneous ratio bi i β I Bi I Either dimension may be negative Examples: 1 Newspapers: reader wealth, advertiser size 2 Software platforms: constant profit ratio, project size For concreteness: newspapers Now b I = PI P I ν I N J + 1 β I ν J µ J ρ J is Spence distortion Sign determined by ν I = sign of b I P I Serve large or small scale readers? Tabloids v. serious papers Different predictions on effects of competition, discrimination Predicts complementary participation for serious papers Empirical data now very useful

18 Policy applications General case Conclusion Identifying market power, predation 1 How to figure out market power? Use Lerner index 1 On one side individually, with value to marginal other P I (C ) I +cn J b J N J P I Not much more complicated, but might want to multiply by P I 2 Or for market as a whole α = ( ba + b B c) N A N B π (1+α)π R fraction of profits from interactions Either casually, or rigorously identify (instruments) 2 Predatory pricing with same approach

19 Regulation Basic Argument Policy applications General case Conclusion Regulation also beyond scope, but a few ideas 1 Ramsey pricing calls for balanced regulation Contrast with net neutrality, interchange regulation Requires much information, simpler just to avoid harm... 2 May favor quantity to price regulation Like anytime price capped with quality unregulated Here worse, because quality is other (distorted) users! Except when interaction costs (especially with surplus) Forced tabloid subsidies = advertiser P Tends to favor quantity regulation Distorts less other sides, encourages recruitment Best if market power worst on one side, Spence unknown 3 Price discrimination helps with Spence, extra benefits Except with negative Spence distortion

20 General model Basic Argument Policy applications General case Conclusion So far: special model, but arguments quite general Only need to maintain four assumptions: 1 Exogenous, quasi-linear utility 2 Differences in value to other side 3rd-degree discriminated 3 Exogenous marginal prices 4 Externalities only to participants Demand Supply Easy to eliminate (generalizes Segal 1999), but not relevant Arbitrary number of sides One-sided net., 2sms with within-side effects, hetero. value Arbitrary finite, smooth, quasi-linear utility u I ( N; θ I) Arbitrarily (smoothly) heterogeneous Arbitrary smooth cost C(N)

21 General pricing Basic Argument Policy applications General case Conclusion Again, insulating tariff (just insulate against more) Only need enough to make graph acyclic... Thus analysis simple (essentially same, via allocation) Social pricing P I = Private pricing P I µ I + }{{} classical marginal revenue J C }{{} I ui J NJ marginal cost J }{{} marginal externalities u J I NJ }{{} cross-marginal revenue = C I }{{} marginal cost

22 Discussion Basic Argument Policy applications General case Conclusion This suggests three things 1 RT2006 special, but analysis general Dimensions of heterogeneity RT2006 allow are right ones Important in empirics via random coefficients Spence distortion generally what matters Even true for comparative statics Depends on exogenous marginal price, other assumptions 2 Allocation approach general 3 Solves maybe oldest theory problem in network economics Liebowitz and Margolis (1994): does monopoly interalize (neutralize) network externalities? Yes...but imperfectly because of Spence

23 Directions for future research Policy applications General case Conclusion Paper aspires to make two contributions 1 Simplify, generalize analysis 2 Importance of source of user heterogeneity Many directions left for future research Empirical applications: which models fit, test predictions Direct important extensions 1 Externalities to non-participations 2 Regulatory design Two big, open theoretical questions 1 Revenue maximizing matching (market design meets 2sms) 2 Tariffs, coordination and market power